Complete identification of products of the reaction 20Ne + 12C at 110 Mev

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Submitted on 1 Jan 1977

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Complete identification of products of the reaction 20Ne

+ 12C at 110 Mev

J. Menet, A.J. Cole, N. Longequeue, J.J. Lucas, G. Mariolopoulos, J.B.

Viano, J.C. Saulnier, D.H. Koang

To cite this version:

COMPLETE

IDENTIFICATION OF

PRODUCTS

OF THE

REACTION

20Ne

+

12C

AT 110 MeV

J. MENET, A. J.

_COLE,

N.

_LONGEQUEUE,

J. J.

LUCAS,

G.

MARIOLOPOULOS,

J. B.

_VIANO,

J. C. SAULNIER and D. H. KOANG

Institut des Sciences Nucléaires

_(IN2P3

et

_USMG)

B.P.

257,

Centre de

_Tri,

38044 Grenoble

_Cedex,

France

(Reçu

le 2 mai

1977,

accepté

le 18 mai

₁₉₇₇₎

Résumé. ₂₀₁₄ L’identification _complète des _produits de la réaction 20Ne (110 MeV) + 12C a été

faite en utilisant un _temps de vol et un _telescope 0394E - E. Les distributions

_angulaires

des _produits

de réaction et leur _spectre en _énergie étaient obtenus à des _angles

_compris

entre 3,7° et 17° _(Lab).

La section efficace mesurée des résidus

_{d’évaporation}

est de 1 270 ± 150 mb.

_L’analyse

des résultats

a été faite en utilisant un formalisme Hauser-Feshbach

_dépendant

du moment

_angulaire.

Abstract. 2014

Complete identification of

_products

of the reaction 20Ne (110 MeV) + 12C has been carried out

_using

time

_{of flight}

and 0394E - E measurements.

_Angular

distributions of reaction _products and _{energy spectra} were obtained between _{laboratory angles} of 3.7° and 17°. The

_evaporation

residue

cross-sectionwas measured to be 1 270 + 150 mb.

_Analysis

of the data has been carried out

_using

the Hauser-Feshbach _angular momentum

_dependent

formalism.

Nuclear reactions

_12C(20Ne,

_X)

E = 110 MeV. Simultaneous identification in mass and

_charge.

Measured

_yields,

_{energy spectra} and

_angular

distri-butions for 6 A 32.

_{Evaporation analysis.}

Classification

Physics Abstracts 25.70

1. Introduction. -

Increasing

attention has been focused

_recently

on

_composite

_systems

_produced

in reactions between

_heavy

ions

_[1].

Measurements of the cross-section for formation of a

_compound

_system as a

function of _energy have been used to

_explore

the fusion barrier

_[2]

and the results have been

_interpreted

in

terms of a critical

angular

momentum

_[3]

or a critical

radius

_[4]

_beyond

which no

compound

nucleus

forma-tion takes

_place.

In

_heavy

and

_{medium-weight}

compo-site _systems some

_study

has been made of

_strongly

inelastic _processes

_{[5, 6]}

_including

fission

_[7]

and

quasi-fission

_{[8, 9]}

which

_together

with

_complete

fusion and direct reactions make _up the total reaction

cross-sec-tion. The

_strongly

inelastic _processes become more

important

with

_{increasing bombarding}

_energy. The

_simple

method of

_measuring

fusion

cross-sections in which individual reaction

_products

are not

identified

_[2]

encounters serious difficulties if

_applied

to

light

composite

systems since

_evaporation

residues

following compound

nucleus formation _may be confused with

_products

of

_strongly

inelastic collisions. The situation is

_{improved by}

identification of mass or

charge

of the

_products

_{[9, 10]}

since the _{energy spectra} for fusion

_products

are centered almost

_exactly

around the energy

corresponding

to the

_velocity

of the

recoiling

nucleus.

Furthermore,

data obtained in this

way may be

compared

to fusion

_evaporation

calcula-tions

_using

statistical models. A further considerable

improvement is,

of course, obtained if

charge

and mass are identified both from the

_point

of view of statistical

model

_predictions

and for the identification of the mechanism

_responsible

for low

_{yield products}

which

may otherwise be obscured

by

neighbouring isotopes

(isotones).

Up

to the

_present,

few articles have

_appeared

in the literature in which

_complete

identification of both

mass and

_charge

was made.

_Apart

from the work of the

Strasbourg

group

[11]

we know of

_only

one such

publication [12].

In this work

_{Weidinger et}

al.

mea-sured _energy

_spectra

at

_angles

between 20 and 220 for two reactions :

16O

+

160

and

160

+ 12 C

at an

incident 160

energy of 60 MeV.

Cross-sections,

energy

spectra, and

_angular

distributions of the

_completely

identified

_product

nuclei were

_compared

to Hauser-Feshbach calculations. Overall

_good

_agreement was

obtained

_using

the level

_density

_parameters

of Gilbert and Cameron

_[19].

However the cross-sections for

evaporation

residues for the

_lightest

nuclei observed

1052

were not well

_predicted

and the

_{predicted angular}

distributions were also

_{disappointing.}

The

_bombarding

energy was low

_enough

so that little contribution was seen from _processes other than direct reactions and

compound

nucleus formation.

Nevertheless,

from the

point

of view of the statistical

_analysis,

the results

clearly

showed the need for

_complete

identification of the

_products.

_Furthermore,

the double

_humped

struc-ture

_produced

in _{energy spectra} at small

_laboratory

angles

due to the

_evaporated

_{alpha particles}

would

probably

not have been observed had

_{only charge}

been identified.

We _report in this _paper the first of a series of

measu-rements on the

z°Ne

+

12C

_system with

_complete

identification of the reaction

_products.

Some

measure-ments

_{including charge}

identification

_already

exist

_[22]

at 80 MeV and the elastic

_scattering

has been studied

quite extensively [14].

The

_experiments

were

_begun

in

the

_hope

of

_obtaining

information on nuclear level densities for

_light

nuclei. Furthermore the

_strongly

inelastic _processes in

_light

_systems have as _yet received little attention. Thus our aim is to understand the fusion _process at

_relatively

low

_energies

in order to

extrapolate

this

_{understanding}

to

_{higher energies}

where non

_compound

_processes are

_expected

to

become

_important.

It should also be

_interesting

to compare the systems

2°Ne

+

12C

and

160

+

16O

although

the detailed

_comparison

will

_require

data

over a wide _{energy range} for the two _systems. We

describe here the measurement and

_analysis

of the

2oNe

+ 12 C

reaction at 110 MeV incident _{Ne energy.} The

_experimental

_arrangements are described in

section 2 and the results in section 3. The

_analysis

of that _part of the cross-section attributed to

_compound

nucleus formation is

_given

in section 4.

_Finally,

section 5 summarizes our main conclusions and direc-tions for further

_study.

2.

_Experimental

method. - The

experiment

was

carried out

_{by directing}

a 110 MeV

2°Ne

beam from the Grenoble

_cyclotron

onto a self

supporting

carbon

target

(200

_Jlg/cm2)

on which was

_evaporated

8

_Jlg/cm2

of

_gold.

Absolute cross-sections in the

20Ne- 12C

reaction were obtained

_by

normalizing

the data to the elastic (assumed to be

_Rutherford)

_scattering

on the

gold layer,

the thickness of which was measured

_by

comparing

the elastic

_scattering

with that from a

reference (100

_Jlg/cm2)

_gold

_target.

Beam currents were measured in a

_Faraday

_cup of

internal diameter 12 mm

_covering

an

angle

of ±

30,

which was sufficient to

_accept

the collimated beam in the

_scattering

chamber. The

_target

thickness was

monitored

_during

the

_experiment

_using

a detector

situated at 170 to count elastic events relative to

Faraday

cup counts.

The detection _system was mounted on a rotatable arm connected to the

_scattering

chamber via a

sliding

seal. Identification of 20 nuclei 6 A 32 was

accomplished

by

measurement of time of

_flight

t,

energy

loss,

AE,

and residual energy, E. The AE detec-tor consisted of an ionization chamber of 100 mm

length

filled with an

_{argon-methane}

mixture (90

_%

_Ar,

10 %

_CH4)

at a _pressure of 40 mm of

_Hg.

The chamber entrance window was made of a 40

Jlg/cm2

formvar

foil mounted on a metallic

_grid

which transmitted 85

_%

of the incident

_particles.

The E measurement was

accomplished using

a

_{low-resistivity}

silicon detector of 200 _pm thickness and 450

mm2

surface area.

The

_{time-of-flight}

of the reaction

_products

was

measured over a

_{flight path}

of 292 cm. The start

_signal

was

_{produced by}

a channel electron

_multiplier

which

detected electrons liberated

_by

the _passage of a

_heavy

ion

_through

two 10

_Jlg/cm2

carbon foils

_(Fig.

_1).

Electrons were accelerated between the foils and the tube

_by

a 1 kV electrostatic

_potential.

The rise time of this device was

_typically

6 ns. The

_stop

_signal

was

taken from the E detector which was mounted at the back of the ionization chamber.

FIG. 1. - Start detector. ₁₎ 10 _pg/cm2 carbon foils at a _potential

of 1 kV. ₂₎ Prism _supporting the foils. ₃₎ Electron channel multi-plier operating at 3 kV. 4) Trajectories for electrons ejected from the carbon foils during the passage of reaction products. The electrons are accelerated _by the 1 kV _potential between the foils

and the collecting cone of the electron multiplier. The solid

_angle

of the detection _system was limited

by

the ionization chamber entrance window. The carbon foils were

_{large enough}

in area so as to

_average

out small

_{angle scattering gains}

and losses at the DE

entrance window. Likewise the E detector was

large

enough

to detect _any

_{particle passing through}

the AE

detector.

The electronics were set _up before the

_experiment

using

a

244Cm

oc source

(106

_counts/s

into 4

_7r).

The , time resolution was - 1.2 ns for these a

_particles

(5.8

MeV)

and

_{approximately}

700 _ps for the

_elastically

scattered

2°Ne.

The detection

_angle

was determined to within 0.20

by comparing

the _energy difference between the elastic

scattering

from the carbon and

_gold

of the

_target.

The electronic

_stability

was monitored

_by

_observing

_AE,

E and t

_{peaks corresponding}

to elastic

scattering

from the

_gold

_target

_layer

in a multichannel

_analyser.

An

on-line

_computer

_system was used to calculated the

and AE +

_{pE where p}

was chosen so that DE +

_uE

was

_{approximately}

constant for a

_given

nuclear

charge

Z. The mass and

charge

information was

displayed

as a function

of v2

in a

_biparametric

repre-sentation

_during

each run

_(Fig.

_2).

_Finally

the

_quan-

tities

E,

AE +

_{JlE, t,}

(E +

_{âE) t2,}

and

V2

were stored

on

_magnetic

_tape.

The mass resolution for

_particles

of 2

_MeV/nucleon

was

AM/M

= 1.7 x

10-2

and the

charge

resolution, AZ/Z

= 3.5 x

10-2

_(Fig.

_3).

FIG. 2. -

Example of _{biparametric spectrum. a) Charge} identi-fication AE + pE versus v2. _b) Mass identification (AE + E) t2

versus V2.

From the

_{biparametric representations (Fig.}

₂₎

it

was an _easy matter to set mass and

_charge

limits for

each nucleus. With these limits the

_magnetic

_tapes

were

processed

for the _{energy spectra} of each nucleus. A low _energy cut-off of 0.6

_{MeV/nucleon imposed by}

the AE detector

was

_{apparently sufficiently}

low so that

all the cross-section was

_effectively

measured. The

incident

2°Ne5+

(110

_MeV)

beam was contaminated

by 5 %

of

1604+.

_{Using experimental}

results for

16O

on

12C

(60

MeV)

we have estimated that this contamination does not introduce more than a 5

_%

error in the measured residue cross-sections.

The 160

and

2°Ne

elastic

_{peaks permitted}

the absolute cali-bration of the AE and E detectors.

3.

_Experimental

results. - 3.1 CRITICAL

ANGULAR MOMENTUM. - Measurements were carried out

bet-ween 3.70 and 170 in the

_laboratory.

_Energy

_spectra

at 4.20 are shown in

_figure

5. Identification of the

evaporation

residue

_part

of the cross-section was made

from the form of the _energy

_spectra

and

_angular

dis-tributions. This

_procedure

was

_particularly

impor-tant for

2°Ne

and

_{24Mg. 24Mg}

could be

_produced

either

_by

a

_particle

transfer or

_by

fusion followed

_by

evaporation

of two

_alphas

or one

_alpha

and four

nucleons. The fusion

_evaporation

contribution was

centered around the _energy

_{corresponding}

to the

velocity

of the

_{recoiling compound}

nucleus. We

therefore assumed that the

_high

_energy

_peak

in the

24Mg

spectrum

(Fig.

5c)

corresponded

to an a transfer

with a

_Q

value of - - 15 MeV. This contribution

FIG. 3. -

Typical spectrum of mass and _charge identification at 6° lab for v’ _{corresponding} to the _{average velocity} of the _recoiling

compound nucleus 32S.

FIG. 4. - 2°Ne

energy spectra (a, b) and angular distribution (c). The arrows in the _{energy spectra} indicate the energy corresponding

to the velocity of the _recoiling 32S nucleus.

integrated

over the

_angular

distribution amounted

to 24 mb. The

20Ne

_energy

_spectra

were more difficult

to

_interpret.

At

_{large angles}

a fusion

_evaporation

contribution was

_{clearly distinguishable (Fig.}

4b)

But

1054

featureless _energy distribution

_extending

from the elastic

_peak

down to the

_experimental

low _energy out

off (Fig.

4a).

The

_evaporation

residue contribution was

estimated

_{by using}

the

_shape

of the

_angular

distribu-tions from

_neighbouring

_isotopes

to

_extrapolate

the

FIG. 5. -

Recoiling nuclei _{energy spectra} at a _{laboratory angle} of

4.20. In the _figure the arrows indicate the _{energies corresponding} to

the _compound nucleus recoil velocity.

residue cross-section to small

_angles.

The value obtained was 200 ± 50 mb

_(2°Ne).

The total

_evaporation

residue cross-section was

obtained

_{by summing}

all the

_evaporation

residue reaction

_products

for A > 20. The value obtained

was _6ER = 1 270

± 150

mb. The measured

cross-sec-tions for each

_isotope

are

_given

in table I.

_Practically

TABLE I

Partial

_evaporation

residue cross-sections,

in millibarns

no cross-section was found for masses 20 with the

exception

of

160

coming

from the beam contamina-tion or from a transfer.

_Integration

of all reaction

products

excluding

the

2°Ne

elastic cross-section

gave a value for the total reactions cross-section of

dp = 1 700

± 170

mb.

If,

_{as seems}

probable,

the

evaporation

residue cross-section is

_equal

to the

compound

nucleus formation

_{cross-section,}

we deduce

a value of the critical

_angular

momentum for

compound

nucleus formation in the

sharp

cut off model of

_1,,r

= 23. An

optical

model calculation

using

the _energy

_{dependent potential}

_parameters of

Van-denbosch

_[14]

_gives

Op = 1 806 mb _at 110 MeV in

good

agreement

with our

_experimental

value. We note

that

_{75 %}

of the total cross-section at 110 MeV

corresponds

to fusion and that most of the

_remaining

cross-section

_corresponds

to inelastic

2°Ne

events.

3.2 ENERGY SPECTRA

_(Fig.

_5).

- We

observe

essen-tially

two main

_types

of _energy

_spectra

for evapora-tion. The

_first,

_{corresponding}

to nucleon

_evaporation,

consists of a bell

shaped

structure centered around the value

_ER

_{corresponding}

to the

_compound

nucleus recoil

_velocity.

The

second,

which is more

_pronounced

at small

_angles,

consists of a double

_humped

structure

again

centered around

_ER

and

_{corresponding}

to events

in which an a emission in the forward or backward

observed structure is

_produced.

This is due to the relative smallness of the recoil momentum

_produced

by

nucleon

_evaporation

as

_compared

with a

evapo-ration. These conclusions are

_generally

confirmed

_by

detailed calculations

_{(section 4)}

and are

_extremely

useful since

_they

allow

_qualitative

conclusions to be made

_{simply by}

examination of the residue _energy

spectra.

Their

_application

_may be illustrated with reference to

_figure

5 which shows _energy

_spectra

measured at

_elab

= 4°2.

Si (Fig. 5a) :

four

_{principal isotopes}

2 6,2 7,2 8,2 9 Si

were

observed.

All _spectra are centered

_{around Er.}

The

28Si spectrum,

which is similar to that

_{of 29Si,}

is cha-racteristic of nucleon

_evaporation

since no structure is observed

_(1).

Furthermore

_single

a

evaporation

from

32S

would

_produce

28Si

excited well above the

particle

emission threshold. In contrast,

26Si

and

2’Si

appear to contain a

_strong

a-nucleon

_evaporation

component.

Al (Fig. 5b) :

again

four

_{principal isotopes}

25,26,27,2 Al

were observed. The

28Al

_spectrum

is,

as

expected,

characteristic of nucleon

_evaporation

while the mass 25 and 26

products

show the

_typical

a-nucleon form. The non characteristic form of

the 2’Al

_spectrum

suggests

contributions from both a-nucleon and five nucleon processes.

Mg

(Fig.

5c) :

four

_isotopes

_{23,24,25,26Mg}

were

observed. The

masses

_26,

25 are characteristic of

a-nucleon _processes. The _energy

_spectra

of the

masses 24 and 23 are not characterized

_by

_any

_simple

form. Indeed the situation is rather

_complex

since a 2 a process may contribute. In this case the

_angular

distri-butions for each of the

_evaporated

a

_particles

_may

_play

an

_important

role in determination of the final residue

energy

spectrum.

In the case of

24Mg

the situation is

further

_{complicated by}

an a transfer contribution.

Na

(Fig.

5d) :

we observed

_principally

two

iso-topes

11,2 ’Na.

Both have _energy

_spectra

_extending

over a wide _{energy range} and centered

_roughly

around

_ER.

A

_high

_energy shoulder is _apparent in the

_{23Na spectrum.}

The

_{non-symmetrical}

character of these

_spectra

indicate that at least one a was

evaporated

in the _{de-excitation process.}

3. 3 ANGULAR DISTRIBUTIONS. - The

experimental

angular

distributions for the most abundant

_product

nuclei are shown in

_figure

6. The widths of the

angular

distributions increase with the difference between the

mass of the observed residue and the

_compound

nucleus,

due to the increase in the transverse

momen-tum transferred to the residue

_during

the

_evaporation

process.

Exceptions

to this rule can however occur

when a emission _competes with 4 nucleon emission.

An

_exception

to the

_general

form of the measured

angular

distributions occurs for

2°Ne

_{(Fig. 4c).}

At

large angles

(between 8° and

_16°)

the

2°Ne

_angular

FIG. 6. _{- Experimental angular} distributions. The solid lines

which have been drawn to _guide the eye suggest that the cross

sections _{da/dO go} to 0 at 0°. As discussed in the text this is not

neces-sarily true. IIl cach case _{the upper} curw represents the 5ummed cross-section.

distribution resembles that of

_neighbouring

_isotopes.

However at small

_{angles figure}

4 shows that the

cross-section rises

_rapidly

and is

_apparently

not charac-teristic of a fusion

_evaporation

_{process. In}

fact,

the

angular

distribution resembles that of

_deep

inelastic reactions seen in other studies

_[9].

4.

_Analysis.

- 4.1 PROGRAMME

PARAMETERS AND ISOTOPIC DISTRIBUTIONS. - The

analysis

of our

experi-mental results was carried out

_using

the

_evaporation

code GROGI 2 of Grover and Gilat

_[13].

The use of this _programme

_which,

at each

_evaporation

_step,

carries out an

_angular

momentum

_dependent

Hauser-Feshbach calculation has been described in

refe-rence

[12].

The calculations

_{permit evaporation}

of neutrons,

protons,

a

_particles,

and _{y rays.} At each

evaporation

step

the _program

_{requires specification}

of level densities in each

_daughter

nucleus and

cor-responding

transmission

_{coefficients,}

_TI,

for

_particle

emission. Widths for

_dipole

and

_quadrupole

y ray

emission are also

_required.

The

_population

in

_angular

momentum _space of the

compound

nucleus was obtained

_using

a

sharp

cut-off

model. Thus the

_partial

cross-sections for

_compound

nucleus formation were taken _{as a, =}

_{’ltx2(2 I + 1)}

for I

_{fcr and a,}

= 0 for I _>

lrr.

The critical

angular

momentum

_1,,r

was obtained from the measured fusion

cross-section

_using

the same model :

Our measured value of UF = 1 270 mb

1056 1-n e m 3 r a

C41,

I l 0--4 1 E

nti

LE

n .4 e

pa

t o

TAB

del

s

ical

c

Opi

6] e[ a re fe s f 0

ete

U ra pa di ra U the M) C! eas

i

ncr

...,

i

-e ar by

db

ine

cd o ti C U ot

po

S .,,

th t

ns 0 ’S

calcul

cal

+121/3)

0

ls t

nds t

CD

2 0

35(

1.3

8 ial t s_al

ten

e * *

Some

_{justification}

for the

_sharp

cut-off

approxima-tion was

_{provided by}

an

_optical

model calculation

using

the _energy

_dependent

_parameters

of Vanden-bosch et al.

[14]

at 110 MeV. The calculated T values differ from

_{unity by}

not more than 1

%

_up to I = 23.

The

transmission coefficients at each

_evaporation

step for nucleons were calculated

_using

the energy

dependent

parameters of Becchetti and Greenless

_[15].

The a _parameters which were assumed to be _energy

independent,

were taken from references

_[16]

and

_[17].

All

_optical

model _parameters are summarized in

table II. The y widths were normalized in the same _way as in reference

_{[12] :}

thus the reduced width was taken to be 0.3 eV for a

dipole

transition and 0.01 eV for a

quadrupole

transition at 8 MeV excitation. Test

calculations showed that

_predictions

were somewhat

insensitive to these

_parameters.

Level densities were calculated

_using

the formula

proposed by

Lang [18]

which is written in terms of a

level

_density

_{parameter, a,}

and a

spin

_{parameter R}

such

that aR = 2

111ï2

where I is the _moment of inertia of

the nucleus considered. For a we have used the Gilbert

and Cameron

_[19]

_{approximation}

where A is the nucleus mass number and S is a shell

correction. Values of S were obtained when

_possible

from reference

_[19]

and were otherwise

extrapolated

from the tabulated values. The Yrast

_energies

below which the level

_density

is zero for a

_given

J were either

calculated from the formula

or for low

energies

taken from

experiment

[20]. 6

is the

pairing

correction tabulated in reference

_[19].

The

parameter

was fixed

by

requiring

that the moment

of inertia was that of a

_{rigid sphere :}

There is some evidence

[21]

in fusion

experiments

on

light

nuclei that the limit to

_compound

nucleus for-mation at a

_given

excitation _energy is

given by

the Yrast line i.e.

_ler

=

lYRAST.

Since a measurement of the fusion cross-section for

2°Ne

on

12C

has been made

at 80 MeV

_[22]

we have

supposed

that the

Icr

obtained

from this work

_corresponds

to

_1YRAST

at the

corres-ponding

excitation _energy of 49 MeV. With this

supposition

we find _ro = 1.3 fm.

We remark that the calculations are

_extremely

sensitive to the

_positions

of the Yrast line. Thus a

calculation made

using

the

_{liquid drop}

moment of inertia

_[23]

failed to account even

_{qualitatively}

for our

data.

_Essentially

this failure was due to

_high

level densities which

produce

enhanced nucleon emission

FIG. 7. -

Experimental cross-sections for the principal isotopes

(full lines). The arrows and dashed lines are the results of different calculations using the GROGI 2 code as _explained in the text.

As can be seen in

_figure

7 (dotted

lines)

the measured cross-sections are

_{qualitatively reproduced}

_by

the calculations. A detailed

_description

of the

_evaporation

chains

_leading

to each

_product

is

_given

in table III. The observed

_{discrepancies}

seem to be due

_(as

noted in ref.

_[12])

to an underestimation of the

_a/nucleon

evaporation

ratio. Thus somewhat better

_agreement

was obtained

_{by increasing}

the a

optical potential

radius thus

_reducing

the Coulomb barrier and

increas-ing

the

_{corresponding}

transmission coefficients. (These calculations are indicated

_by

arrows in

_figure

_7.)

However no detailed

_exploration

of the _parameter space was carried out. There are two reasons for this.

Firstly

the calculations are rather

_long

and

_expensive.

Secondly,

as will be seen in the

_following

_section,

it is

impossible

at _present to use measured

_angular

and energy distributions in order to constrain the

para-meters of the model.

4.2 ENERGY SPECTRA AND ANGULAR DISTRIBUTIONS. - In

principle,

measurement of _{energy spectra} and

angular

distributions

_provide

_strong constraints on

predictions

of

_evaporation

models.

However,

the construction of these

_quantities

from the

_evaporation

model

_predictions

_presents

a number of

problems.

Firstly,

for each

_evaporation

in a

_given

_chain,

the

angular

distribution of the

_evaporated

_particles

varies in

_principle

with its _energy

_[24].

Since GROGI 2 does

not

_predict

_angular

distributions,

it is _necessary to

assign

some

arbitrary

angular

distribution to each

evaporated particle

in the chain.

_Secondly

the

cons-truction of the resultant center of mass recoil

momen-tum for more than one

evaporation

is somewhat

lengthy

and involves introduction of further

hypo-theses

_expressing

the fact that the

_evaporations

cannot

be considered as

independant

events. These constraints should

_properly

be

_applied

to both the _energy and the

angular

momentum

_populations.

In this first article we avoid these

problems by

adopting

the

_philosophy

of reference

_[12].

_Thus,

explicitly,

we assume

_isotropic

c.m.

_angular

distri-butions for the

_evaporated

_particles.

In this case the

resultant centre of mass recoil momentum for two

successive

_evaporations

_may be written as :

where

_H1(Pl)

and

_H2(p2)

are

_respectively

the

momen-tum

_spectra

for the first and second

_{evaporations.}

The condition of non

_independance

of successive evapora-tions was

_{expressed by requiring}

that the final nucleus

is left at a

positive

or zero excitation _energy. Thus for

two

_{evaporations,}

we have :

where

Ex :

excitation _energy in the

_compound

_nucleus,

El :

kinetic _energy of the first

_particle

in c.m. _system,

TABLE III

1058

E2 :

kinetic _energy of the second

_particle

in c.m.

system,

Q1

and

_{Q2 : Q}

values

_{corresponding respectively}

to

the first and second

_{evaporations.}

The formula _may be iterated

_provided

the above constraint can be modified to take account of a third

evaporation.

We have included such a modification

by requiring

that the _parent

_nucleus,

after the second

evaporation,

has an excitation _energy

_{sufficiently high}

so that

_evaporation

of a third

_particle

(with an _average energy

given by

the

_{evaporation model)}

leaves the final nucleus at a

_positive

(or

zero)

excitation _energy. Thus for three

_evaporations

we

_{require :}

where

E3 :

mean _energy of the third

_particle,

Q3 : Q

value

_{corresponding}

to the third

_evaporation.

The transformation of

_{H( p)}

to the

_laboratory

system

permits

calculations of _energy

_spectra

and

angular

distributions.

_Examples

of _{energy spectra} are

shown in

_figure

8. The calculations lend

_support

for the

_qualitative

conclusions made in section 3.

However,

the

_predictions

are somewhat

_{disappointing}

in detail. The

_prediction

shown in

_figure

8

for 26Al

_may

be

_{improved by assigning,}

as in reference

_[12],

a non

isotropic angular

distribution to the c.m. resultant recoil momentum. We feel it is rather difficult to

justify

such a

_procedure

since the

_{degree of anisotropy}

is unknown. It is

_possible

for

_example

to obtain

FIG. 8. -

Energy spectra and calculations for isotropic c.m. recoil

(full line), I /sin 0 recoil (dot-dashed line) and 1/sin2 0 recoil (dashed line).

resultant recoil

_angular

distributions with an

aniso-tropy greater

than the

_1/sin

0 limit

_usually

assumed for

single evaporations.

Furthermore of course, as

men-tioned above the

_{anisotropy depends}

in

_principle

on

the _energy

_(energies)

of the

_{evaporated particle}

(particles). Figures

8, 9

show the effect of

_increasing

the

anisotropy

of the c.m.

_angular

distributions for the

case of

29Si

and

26 Al

for both small

_angle

energy

spectra and

_angular

distributions. An

_important

FIG. 9. -

Angular distributions and calculations for _isotropic c.m.

recoil (full lines), 1/sin 0 recoil (dot-dashed line) and _I/sin’ 0 recoil (dashed lines).

remark should be made in this context, i.e. for a

resul-tant recoil momentum with a

_1/sin

0 or more

aniso-tropic

angular

distribution,

the

_laboratory

cross-section

_da/dOlab

does not _go to zero at

_Olab

= 0 _as is

sometimes assumed in evaluation of fusion

cross-sections. An allowance for this effect has been included in our estimate of the fusion cross-section error.

As far as detailed

_comparison

of our measured

angular

distributions with

_evaporation

model pre-dictions is

concerned,

our conclusion is that such a

comparison

is not useful unless the construction of the resultant recoil

_angular

and momentum c.m.

distri-bution is carried out

_correctly

within the context of the model. In

_particular

we consider it

_impossible

to

decide if the

_{discrepancies}

obtained in this work and in

some cases in reference

_[12]

are due to failure of the

evaporation

model or to

_{approximations subsequently}

introduced in the calculations.

In summary detailed conclusions

_concerning

angu-lar and _energy distributions must await the

develop-ment of more

_{sophisticated}

methods of

_analysis.

5.

_Summary

and conclusions. - In this article

we

have

_presented

results on the simultaneous

charge

and mass identification of reaction

products

from 110 MeV

2°Ne

bombardment

of 12C.

Energy

spectra,

angular

distributions and cross-sections for 20

_isotopes

have been obtained.

_Apart

from the

_isotopes

_160,

2oNe

and

_24Mg,

the observed _spectra are

characte-ristic of a fusion

evaporation

mechanism. The

measur-ed reaction cross-section is in

_good

_agreement with the

optical

model

_prediction

and the measured fusion cross-section leads to a value of

_hr

= 23 h in the

sharp

cut-off model. The measured

isotopic

distribution are

in

_qualitative

_agreement with

_angular

momentum

dependent

Hauser-Feshbach model

_predictions.

Such models _{may be used} to deduce

_properties

of

_highly

excited nuclei with

_large

_angular

momentum. The data are extensive and in

_principle

_provides

not

_{sufficiently sophisticated}

to enable a

_thorough

exploitation

of the measurements. In this context a Monte Carlo calculation would be of considerable value

_provided

the _proper inclusion of the

_angular

distribution of the

_{evaporated particles}

at each

eva-poration

step is not too time

_consuming.

Finally

there is _strong indication in the

_24Mg

and

_{2°Ne spectra}

of a contribution from a

_highly

inelastic _{process. For}

2°Ne

the observed cross-section for the _process is 400 mb. However we see no marked

variations of the

_angular

distributions of the non

fusion cross-section as a function of _energy and it is

thus not evident that this _process is the same

_deep

inelastic

_scattering

observed at

_{higher energies}

and for heavier

_projectile

_target combinations.

In our

_opinion

measurements at other

_energies

both above and below 110 MeV should be made and

ana-lyzed

more

_thoroughly

in the context of the statistical model. We also _expect an increase in non fusion processes at

_{higher energies.}

Such measurements, when combined with those

_reported

here,

should

provide

severe tests of

_proposed

level densities in

_light

nuclei as well as information on

_non-compound

processes in

light

systems which at the _present time is rather scarce.

Acknowledgments.

- Our

deepest

thanks _go to M. Pierre Oustric who

_provided

the

_{technical, support}

for the

experiment

and in

_particular

constructed the detection

_system.

We would also like to thank members of the PDP

_computing

team for invaluable assistance with data

_acquisition

and reduction programmes.

Finally

we thank Dr. Ed. Gross for a careful

_reading

of the

_manuscript.

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